document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464769>Question 464769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 34cm, and the diagonal is 13cm. Determine the lengths of the sides of the rectangle. \r<BR>\n" );
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document.write( "I need to set this up in a quadratic equation then solve. I have several problems like this and knowing how to set them up would be a big help. Thanks.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318414 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the 5-12-13 triangle sticks out at you, and you recognize 5+12 = 17, times 2 is 34, you're done.\r<BR>\n" );
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document.write( "To set it as a quadratic, we can let L and 17-L be the length and width (17-L instead of 34-L because the perimeter is 2(L+W) = 2(L + 17-L) = 34). The triangle with sides L, 17-L, and the diagonal of length 13 must satisfy the Pythagorean theorem, i.e.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE L^2 + (17-L)^2 = 169\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2L^2 - 34L + 289 = 169\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2L^2 - 34L + 120 = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2(L-5)(L-12) = 0 \Rightarrow L = 5, 12\">\r<BR>\n" );
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document.write( "This implies the dimensions are 5 cm by 12 cm (note that both dimensions are under L because we can choose either length to be L). </SPAN>\n" );
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